Reliability evaluation algorithm for complex medium voltage electrical distribution networks based on the shortest path

Based on the definitions of feeder terminal node FTN and the shortest path from a failure element to FTNs, it is easy to identify a disconnected section, following which a classificatio

Reliability evaluation algorithm for complex medium voltage electrical distribution networks based on the shortest path

Kaigui Xie, Jiaqi Zhou and R Billinton

Abstract This paper presents a reliability evaluation algorithm for medium voltage radial electrical

distribution networks (EDN) The algorithm is suitable for evaluating reasonably complex EDNs

with multiple subfeeders It applies a fonvard-search-method to identifying the section controlled

by a breaker By applying graph theory and considering the structural features of the EDNs,

methods for searching for the shortest paths from any node to the energy source and between any

two nodes are developed Based on the definitions of feeder terminal node (FTN) and the shortest

path from a failure element to FTNs, it is easy to identify a disconnected section, following which a

classification of the nodes is obtained The reliability indices of the buses, feeders and system are

calculated, based on the nodal classification The developed algorithm has been tested on a number

of test systems and the results show the effectiveness and applicability of the approach

1 introduction

Over the past few decades, power system reliability

evaluation has been mainly concentrated on generation

and transmission The basic reason for this is that

generation and transmission systems are capital intensive,

and their inadequacy can cause widespread catastrophic

consequences for both society and its environment [I-31

Utility statistics, however, show that electrical distribution

network (EDN) failures account for approximately 80% of

the average customer interruptions [I-31 Reliability assess-

ment of EDN is a normal practice in a number of countries

such as Canada, USA, Australia and Great Britain

The analytical techniques required for reliability assess-

ment of an EDN are highly developed [1-7].Tne conven-

tional techniques for the reliability assessment of an EDN

are generally based on failure mode-and-effect analysis

(FMEA) [I, 2,6] The analysis of the failure events and their

effects can be presented in the form of a FMEA table, based

on reliability parameters and network structures, following

which a comprehensive set of reliability indices can be

obtained There is a wide variety of components and

element-operating modes in a complicated EDN with

multiple subfeeders, and it is dimcult to evaluate the

reliability directly from the thousands of basic-failure-event

combinations

There are several available methods for evaluating the

reliability of a complicated EDN Reference [2] presents an

effective approach, designed as the reliability network

equivalent method The main principle in this approach is

that an equivalent element can be used to replace a portion

(D IEE, 2W3

IEE Prowedingr online no 20030797

doi: IO IM9/ipgtd20030797

Paper first rmived 17th June 2002 and in re\iied form 1st July 2W3

K X e and I Zhou are with the College of Electrical Enginmring, Chongqing

Uluvenity, Chongqins P.R China

R Elllinton is with the Power System Research Group, University of

Saskatchewan Saskatoon, Canada

of the distribution network and in tum, decompose the system into a series of simpler distribution systems for

which the reliability indexes are obtained using FMEA A system with multilevel subfeeder, such as rural EDN in developing countries, may require many decomposing and combining operations to obtain the reliability indices of every load point An alternative approach based on the shortest path for reliability assessment in a complex EDN is

proposed in this paper

2

Figure I shows a reasonably complex medium voltage EDN

identifying the classes of nodes

23

16

Fig 1 Complex medim voltage EDN with subfeeden

2.1 Relevant definitions

Definition I : All nodes in a radial EDN except nodes

connected to end loads are named feeder nodes(FNs)

Definition 2 An F N to which none of downstream

direction FNs connected is named a feeder terminal node

(FIN)

686

In Fig 1, nodes 2,3,4,5,6,7,8,11,12,13,18,19,20 and 22 are

FNs, hut only nodes 8,13,20,22 are FTNs

Let S represents the set of nodes of an EDN, SI is a

proper subset of S a n d S2=S/Sl ={x(xeS, hut x e s l }

Definition 3: The nodes, which belong to Si and connect

with nodes in S,, are named the inner-bound-nodes(1BNs)

of SI

The nodes_ which belong to S, and connect with the

nodes in S I , are named the outer-hound-nodes(0BNs)

of SI

Assuming in Fig 1 that the line between node 4 and 11

fails, SI = {4,5,1 l , l 4 } , then the IBNs of SI are {4,5,1 I } and

the OBNs of SI are {3,6,12.18}

2.2 Shortest path between any two nodes

2.2.1 Shortest path from a node to a source:

Starting with a selected node, it is possible to get the shortest

path by searching for the upstream nodes based on the load

flow in the normal healthy state If the shortest path from

node A to the source is PathA, PathA can be described by an

ordered node series Assuming that the source node is C

and S represents the set of all nodes in an EDN

C E PathA(VA t S ) (1)

For example, the shortest path from node 14 to the source

in Fig I is Path14={14,11,4,3,2,1} In a similar manner,

Path24 = { 24,22,19,18,5,4,3,2,1}

Many EDNs are designed with loop structures, but are

operated without loop paths In these cases there is one and

only one shortest path from any node to the source

2.2.2 Shortest path between two nodes: The

approach to determine the shortest path from node A to

node B is as follows Suppose the shortest paths from node

A, and B to the source are PathA and Paths, respectively

Let

Patha = { A , A i , A 2 , , A p - l , A p , .A,+,, c} ( 2 )

Paths = { B : B I , B,, , B q - i , A P , .A,+,, C } (3)

where parameter m is a integer and m 2 0, p and q are two

natural numbers

So Puth~ n Paths # @ ( 4 )

where @ is an empty set

Definition 4: The first element of the set {PathAn

Paths} = {p, , , A,+,,C)(mtO), (i.e the node Ap) is

named: joint node(JNA.B) between PathA and PathB

In Fig 1, rN14-24= {4}, and IN,;.;Z= {Si

Let

PathAI5 ={XI E Patha, butx$Patha}

(50)

PathslA = { B , B I , B,-I} (5b)

={A,.41,A2, J p - 1 )

Similarly,

Let S' represents the reverse order set of S (for example,

The shortest path from node A to node B can be

obtained as follows As the EDN is operated without a loop

path, the shortest path from node A to node B is:

Path~4={1,2,3,4,11,14})

P0tha-a = PathajB C€ JNA-B C€ ( 6 ~ )

= { A , A i r A 2 , , A P - i , A p , B q - i , , B ~ , B I , B } (6b)

where fE represents ring sum of two sets

In Fig I, Path~~={23,22,19,18,5,4,3,2,1}, Patha={8,7,

6,5,4,3,2,1}, then Path23-8= {23,22,19,18,5,6,7,8} and

I€€ Proc.-Gmer T r m Dkrrh Vol 1517, No 6, Noomher 2W3

Path8-z = {8,7,6,5,18,19,22,23] Similarly, Pathl4-27 = (14,

11,4,5,6,27}

2.3 Classification of nodes

Nodes are classified in terms of the effect of a failure on these nodes Assuming a fault has occurred, it is necessary

to search for the switching components that must operate (i.e circuit breakers, reclosers, disconnect/sectionalising switches, tie switches etc)

Nodes are Classified into four types based on the duration

of loss of service in this paper They are: (a) healthy nodes with zero duration out of service; (b) nodes with duration out of service equal to the switching/sectionalising time; (c) nodes with duration out of service equal to the switching/sectionalising time plus the reclosure time of a tie switch; (d) nodes with duration out of service equal to the repair time of the failed component

2.4 2.4.1 Identifying the controlling circuit breaker/ recloser: While a component fails, if the number of failed

components is more than two, it can be identified as a respective event, the first circuit breaker/recloser can be determined by searching for the upstream lines based on the load flow in the normal state The downstream nodes after this breaker belong to classes B, C or D The specific class should be determined The other nodes, including the upstream nodes before this breaker and the other feeder nodes, belong to class A

Assume that the line between node 18 and 19 in Fig I

fails Nodesjl, _ , 17,27 , _, 32) will belong to class A and nodes {18,19 , 26) to class B,C or D If the line between nodes 22 and 23 fails, node 23 will belong to class D and the others to class A because of the fuse

Identifying the classes of nodes

2.4.2 Identifying the controlling disconnect/ sectionalising switches: Identifying the controlling

disconnect/sectionalising switch is the most important and difficult task in the reliability assessment of an EDN It is done after a breaker operation to find those switches required to disconnect the failed component

The shortest path method is applied in this paper to identify the required disconnect/sectionalising switch

If switches exist at both ends of the failed component, for example, the line between node I8 and 19 of the EDN

shown in Fig 1, opening these switches will complete the disconnecting operation If not, a node without a disconnect switch is selected as the start node (SN) Assume the SN is node A and the FTNs are {SI ,B2, ,BM) (A4 is the total number of the FTNs) After searching for the shortest paths

from node A to the FTNs, i.e PathA-sl, Path~-sz , ,

PathR-BM and checlang the disconnect switches on lines

based on PathA-sj, j = 1,2 ,. , M , the first upstream disconnect switch is the proper opening switch, it includes the case of opening the same switch with different paths The same approach is applicable to the shortest path from ~~

SN to the source node

In Fig 1, supposing the line between nodes 4 and I 1 fails

and node 4 is selected as the SN From the above

Patha-1 = {4,3,2,1},Path4_~ = {4,5,6,7,8}, P~thq-13 = {4,1 I ,

12,13}, Path~~x,={4,5,18,19,20), and Parh4-u={4,5,18, 19,22} The appropriate disconnect switches to be opened

wrresponding to Path4_1, Path4-s, Patha-13, Parh4-2o and Patha-2r are those connected to node 3 on line between

nodes 3 and 4, to node 6 on the line between nodes 5 and 6 ,

to nodes 12 on the line between nodes I 1 and 12, to nodes 5

687

on the line between nodes 5 and 18 and to nodes 5 on the

line between nodes 5 and 18, respectively

2.4.3 Forming the separate subsystem: The EDN

can usually be separated into several subsystems after the

failed components are disconnected

In this case by omitting the lines connected to the OBNs

and using the depth-first-search or breadth-first-search

approach [8] starting with every node of OBNs, the node

set of every separate subsystem can be obtained The

structural parameters of each network are therefore formed

based on the primary network

2.4.4 identifying the classes of nodes: From

Section 2.4.1, the upstream nodes before the switching

breaker and other feeder nodes are identified as class A, and

the downstream nodes as in class B,C or D The separate

subsystems are formed by omitting the lines connected to

OBNs In any subsystem, if there exists a node connected to

the source, then the nodes in the subsystem belong to class

B If a node connected to the source does not exist, hut

there is a node connected to the tie switch, then the nodes

belong to class C If there exist nodes connected to neither

the source nor the tie switch, the nodes belong to class D

In summary, the nodes belonging to class A can

be identified using the method in Section 2.4.1 and the

nodcs belonging lo class B,C and D using thc " A d in

Section 2.4.2

classes of nodes is shown in Fig 2

The flowchart for the algorithm used to identify the

3 Reliability assessment algorithm

Based on the above description, the E D N reliability

assessment algorithm is as follows

I Read the primary data and compute the steady state load

flow

2 Enumerate the contingencies

3 Apply the shortest path method to identify the section out

of service after a failure event, and to form the separate

subsystems If there exists a tie switch in the subsystem, add

the tie switch parameters to the subsystem

4 Identify the classes of nodes

5 Compute the abnormal state load flow and check the

voltage constraints at the nodes and the line capacities; if a

violation occurs, take action such as compensating reactive

power If violations still exist after the actions, shed load [9]

6 Based on the classes of nodes and the amount of load

shedding, compute the reliability indexes

7 If all contingencies are not yet considered, go to step 2

8 Deduce the reliability indices of the load points, feeders

and system and print the output

During Step 5, VAr compensation may be required, and

the abnormal state load flow is computed

The proposed algorithm has been coded in VC+ + and the

effectiveness has been verified using a number of practical

power systems

As an example, the test systems developed at the

University of Saskatchewan for a six- bus reliability test

system designated as the RBTS [ 2 4 were studied The

RBTS-BUS6 is a typical complex mral/urban configuration

enumerate a contingency

search for upstream circuit breaker

J

I

I select disconnect switching devices

/-=-

A Subsystem connected to

tie switches

Fig 2 Flowchart for identfyinq c h s e s of nodes

with sub-feeders and it has 40 load points and 2938 customers The average load of this EDN is 10.7155MW

The customer data, equipment outage data, feeder loading

details and the network structure are given in [3-51

The reliability indices of selected load points in the RBTS-BUS6 are shown in Table 1

Table 1: Load point reliability indexes in RBTS-BUS6

Load I (fiyr) Doint

1 0.3302

4 0.3302

8 0.3725

12 0.3595

16 0.2405

18 1.6725

23 1.7115

26 1.7115

32 2.5890

37 2.5598

40 2.5110

11.101 11.101 10.095 10.280 4.189 5.023 5.023 6.709 5.015 6.143 6.165

3.666 3.666 3.761 3.696 1.008 8.401 8.596 11.482 12.984 15.724 15.480

650.7594 662.8580 623.8670 764.9685 909.2688 1393.809 1426.160 3250.696 2504.614 3033.111 4732.236

Table 2: RETS-BUS6 system reliability indexes for different cases

Note: Case A: discomensfusesalternative supply-transform repair

Case B: no disconnectsno fuses-no alternative supply-transform repair

Case C no disconnects-fusesno alternative supply-transform repair

Case D disconnectsno fuses-alternative supply-transform repair

Case E disconnects-fuses-alternative supply-transform replacement

Case F: disconnects-no fuse-o alternative supply-transform repair

The results shown in Table 1 based on the proposed

algorithm are consistent with the results in [4]

The effects on the reliability of four major design factors

are illustrated using RBTS-BUS6 The base case is the

system shown in Fig 4 of [4] The system reliability indices

for the cases considered are shown in Table 2

Table 2 shows that there is considerable disparity in the

indices for the different cases As expected, Case B produces

the worst set of indices, and Case E produces the hest sets of

indices

Comparing Case B with Cases C,F and D, it can be seen

that a number of factor can be used to improve the

reliability of an EDN Installing the fuses will reduce the

influence of a failure on the nodes out of zone-protected

Installing the disconnect switches will reduce the number of

nodes belonging to Class D therefore, some customers can

he restored in service by switching It may be possible to

transfer the customers from the failed section to the

alternative supply, which will convert the nodes belonging

to Class D into Class C The repair time for a transformer is

much longer than the replacement time, and therefore the

difference between the reliability indices for the two cases is

significant It can be seen from the analysis that EDN with

low reliability can be improved by suitable enhancing

measures, such as disconnect switches, fuses, alternative

supplies and the replacement of transformers

The reliability indices for the system shown in Fig 1 were

computed The customer data, equipment outage data,

branch data and reliability parameters are from the RBTS-

BUS2 [3-51 (the load levels were reduced by a factor of 0.3)

The reliability indices of selected load points in Fig 1 are

shown in Table 3 and the system reliability indices are

shown in Table 4

Table 3 Load point indexes of EDN shown in Fig 1

9

15

23

25

27

31

32

1.1120 1.1660 1.1120 1.5612 1.5125 1.1120 1.1660 1.1120

4.047 9.360 6.941 3.644 3.463 7.432 18.155 16.164

4.500 10.914 7.719 5.690 5.238 8.265 21.169 17.974

735.7500 1784.380 960.9702 1706.966 1571.441 1351.302 2635.521 2696.077

The proposed algorithm was applied to the city-zone and Qinan EDNs of the Chongqing Electric Power Corpo-

ration The city-zone EDN has 81 lOkV feeders and 22

10 kV switching stations The system reliability indexes are shown in Table 5 The approach presented in this paper proved to be very applicable and effective in the analysis of these systems

Table5: System reliability indexes of lOkV medium distribution network in Chongqing

syst.cust1 svst.cust) (hrlcustl (kWh/yrl (kWh/yr) 2.320 10.056 4.334 0.998852 1496655.01 1330.36

Table 4: System reliabiity indexes of EDN shown in Fig 1 for different cases

IEE P r o c - G e ~ r Trruwl DiFrra Vol ISO, No 6, Nul;rmber 2W3

5 Conclusions

This paper presents a algorithm, which can he used

to evaluate the reliability of complex medium EDNs

An approach to searching for the shortest paths from

a node to source and between any two nodes is

presented, based on graph theory and the structural features

of EDNs

An approach to identifying the section out of service after

a fault event is presented, based on the shortest path The

classification of nodes is obtained by identifying the sections

controlled by breakers, tie switches and disconnect switches

etc in a subsystem

The proposed algorithm is based on the shortest path

and does not need an equivalent calculation It can be

used to produce reliability indices for the individual load

points, the feeders and the system by direct determination

without a decomposing and composing process The

approach is shown to have both effectiveness and applic-

ability from the results obtained using a number of

test systems

The approach presented can be used to consider the

effects of breakers, fuses, disconnect switches, altemative

supplies and replacing transformers in addition to other

system design elements The proposed approach has good

universality and practicability

This work was supported in part by NSF of China (No

50307015) and Chongqing Science and Technology project

(No 20037951) in China

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4

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IEE Pro<.-Coler Tranrm Dinrib Vol ISO, No 6, Nowmber 2W3